Project Presentation June2010
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METHODS OF CHARACTERISTIC
DESIGNS OF PLANAR ANDAXISYMMETRIC DUAL BELL NOZZLES
ASHISH GARG
Project Advisor : Prof. JOSEPH MATHEW
DEPARTMENT OF AEROSPACE ENGINEERING
INDIAN INSTITUTE OF SCIENCE
BANGALORE
28TH JUNE 2010
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Introduction
Dual bell nozzle is a concept of altitude adaptive nozzle Flow transition from base bell to extension bell occur at high altitude
No side load generation hence stability point of view its good, which is the main issue forother adaptive nozzles such as spike nozzles
Reasons for significant performance gain
Weak over expansion at low altitude so shocks are weak
No moving part
Higher expansion ratio of extension bell than conventional nozzle giving moreperformance gain at high altitude
Nozzle weight is comparatively very less than optimum contour
Some issues
Fast flow transition is required
Aspiration drag due to recirculation zone
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-20
0
20
0 50 100 150 200
-60
-40
-20
0
20
40
60
WidthX
Y
inflection point
base nozzle
extension nozzle
0 50100 150 200
-50
050
-25
-20
-15
-10
-5
0
5
10
15
20
25
X
R
base nozzle
extension nozzle
inflection point
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About Method of characteristic
Its a numerical method for solving nonlinear inviscid,irrotational flow.
Used to convert partial differential equation into ordinary
differential equation
Exist only in super sonic flow
Coincident with mach line
While derivatives of flow properties are discontinuous but
flow properties are continuous Along given line they satisfy compatibility equation
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Region OTR: Starting of source flow
Region TRDC: Radial flow region
Region CDE: Transition region Region EDX: Flow is fully parallel and uniform
Used linearized approximate integral form of MOC
Foelsch Analytical Method
Different procedures used to design
nozzles using MOC
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Anderson Method
Use MOC equations in discretize form along characteristicline
Different procedures used to design
nozzles using MOC
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Shapiro method
Use MOC equations in discretize form along characteristic line
Shapiro use backward c- characterstic to define more accurate
profile
Different procedures used to design
nozzles using MOC
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Comparision of lengths
0 1 2 3 4 5 6-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
X
R
Re
Me=2.5
C+
Length of centered expansion axis symm. nozzleC- characterstic
backward C-
max
-1 0 1 2 3 4 5 6 7 81
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
X
R
Nozzle length comparison for axis symm Me=2.5
Foesch Analytical Method
SOAM with centered expansion
SOAM with Radius of expansion =1.161
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Types of single
and dualbell nozzles
discussed inthesis
Sr.NO. NOZZLE TYPE BASE NOZZLE EXTENSION NOZZLE
1
single bell
optimum wall
2 parabolic bell
3 wedge/straight line bell
4 pressure boundary wall
5 mach number boundary wall
6
double bell
optimum wall optimum wall
7 parabolic bell parabolic bell
8 parabolic bell wedge/straight line bell
9 parabolic bell pressure boundary wall
10 parabolic bell mach number boundary wall
11 wedge/straight line bell wedge/straight line bell
12 wedge/straight line bell pressure boundary wall
13 wedge/straight line bell mach number boundary wall
14 wedge/straight line bell parabolic bell
15 pressure boundary wall pressure boundary wall
16 pressure boundary wall mach number boundary wall
17 pressure boundary wall parabolic bell
18 pressure boundary wall wedge/straight line bell
19 mach number boundary wall mach number boundary wall
20 mach number boundary wall parabolic bell
21 mach number boundary wall wedge/straight line bell
22 mach number boundary wall pressure boundary wall
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2D planar nozzles
Expansion arc boundary condition
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Axis boundary condition = 0, y = 0
Prandtl-Meyer function
Mach angle equation
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Optimum dual bell
Inflection point conditions
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Parabolic Raos bell
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Parabolic dual bell
Inflection point conditions
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Wedge dual bell
Inflection point conditions
Wedge nozzle wall equation
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PW and WP nozzle contours
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Linear pressure variation along nozzle wall
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Characteristic equation of Axisymmetric
nozzles
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Axisymmetric boundary condition
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Axisymmetric Parabolic dual bell nozzle
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Treatment of Special Conditions
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Nozzle weight calculation
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Validation of Coding through FLUENT
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Validation from1D flow relation
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Boundary layer correction[17]
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Boundary layer correction
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Boundary layer correction
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Typical characteristics of dual bell
nozzles
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2D planar optimum dual bell nozzle
INPUTS
base nozzle exit mach number = 3.5
extension bell exit mach number = 5
base bell exit area ratio w.r.t throat = 6.79
extension bell exit area ratio w.r.t. throat = 25
total pressure = 200 bar
total temperature = 2000k
atmospheric pressure = 0.38 bar
Specific heat = 1.4
Throat height = 1
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2D planar parabolic dual bell nozzle
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2D planar parabolic dual bell nozzle
INPUTS
base nozzle exit mach number = 3
extension bell exit mach number = 5
base bell exit area ratio w.r.t throat = 4.235
extension bell exit area ratio w.r.t. throat = 25
total pressure = 200 bar
total temperature = 2000k
atmospheric pressure = 0.38 bar
reference wedge angle = 15 degree
fraction length used of this reference wedge = 0.8
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INPUTS :
base nozzle exit mach number = 3
extension bell exit mach number = 5
base bell exit area ratio w.r.t throat = 4.235
extension bell exit area ratio w.r.t. throat = 25
total pressure = 200 bar
total temperature = 2000k
atmospheric pressure = 0.38 bar
reference wedge angle = 15 degree
fraction length used of this reference wedge = 0.8
Comparisions of PC, CP, PP, CC nozzles
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For PP the parameters are:slope1 : 0.34, slope2 : 0.21, slope3 : 0.41,
and slope4 : 0.25
For PC the parameters are:
slope1 : 0.34, slope2 : 0.21, slope3 : 0.39,
and slope4 : 0.39
For CP the parameters are:
slope1 : 0.323, slope2 : 0.323, slope3 : 0.41,
and slope4 : 0.25
For CC the parameters are:
slope1 : 0.323, slope2 : 0.323, slope3 : 0.39,
and slope4 : 0.39
Comparisions of PC, CP, PP, CC nozzles
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Shock captured by
MOC solution asRef. [8]
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Axisymmetric nozzle
INPUTS
Nozzle type= Dual parabolic nozzle
Total pressure = 200 bar
Total temperature = 2000k
Reference cone angle = 15 degree
Fraction length used of this reference cone = 0.8
Specific heat =1.4
Mach number at the exit of base bell= 4.8
Pressure at the exit of base bell = 0.47 bar
Mach number at the exit of extension bell = 6.6
Area ratio extension = 80.2
Atmospheric pressure = 0.07 bar = desired pressurefor 6.6 mach number
For PP Axisymmetric nozzle, the parameters are:
slope1 : 0.34, slope2 : 0.2, slope3 : 0.5, and slope4 :
0.3
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Separation criteria and calculation of
transition altitudes[9]
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Goals Achieved and Future Work
From the discussion so far in the presentation. MOC code for 2D Planar and
Axisymmetric Dual Bell Nozzles completed with Boundary Layer Correction
and CFD validation of MOC results.
Transition point calculation with respect to altitude has been formulated in
the thesis.
Experiments need to be done on designed contour by MOC to validate
transition analysis and results on Dual Bell Nozzles.
As we have located the shock where the MOC lines are coalescing. Now the
another future task is to incoporate entropy gradient after this shock in MOC
solution for better appoximation of flow field.
For other researchers working on MOC, Unsteady and 3D effect of flowfield can be modelled and can extend this code further with that.
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References
Foelsch, K., The Analytical Design of an Axially Symmetric Laval Nozzle for a Parallel and Uniform Jet, Journalof the Aeronautical Sciences, Volume 16, 1949, pp.161-166,pp.188
Emanuel, G. and Argrow, B. M., Comparison of Minimum Length Nozzles, Journal of Fluid Engineering, Trans.ASME, Volume 110, 1988, pp.283-288.
Anderson, JD., 2001, Fundamentals of Aerodynamics, 3rd Edition, pp. 532-537, pp.555-585.
Anderson, JD., 1982, Modern Compressible Flow with Historical Perspective, pp. 268-270,pp. 282-286.
Shapiro, AH., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol.I, pp. 294-295.
Shapiro, AH., 1954, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol.II, pp. 694-695.
Frey, M. and Hagemann, G., Critical Assessment of Dual-Bell Nozzles, Journal of Propulsion and Power, Vol.15,No.1, 1999,pp. 137-143.
Masafumi Miyazawa and Hirotaka Otsu, An Analytical Study on Design and Performance of Dual-Bell Nozzles,AIAA, 2004
J.O stlund and B. Muhammad-Klingmann, Supersonic Flow Separation with Application to Rocket EngineNozzles, Applied Mechanics,2005,Vol 58,pp 143-177
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Sibualkin, M. Heat Transfer to an Incompressible Turbulent. Boundary Layer and Estimation of HeatTransfer Coefficients at Supersonic nozzle Throats. J. Aeronaut. Sci., 23, No. 2, pp. 162-172, 1956.
A. MCCABE, Design of a Supersonic Nozzle, Reports and Memoranda No. 3440,March, 1964
Abdellah Hadjadj , Marcello Onofri, Nozzle flow separation, Shock Waves (springer) pp.163169,2009
Coles, D. E. "The Turbulent Boundary Layer in a Compressible Fluid." RAND Corporation Report R-403-PR, September 1962.
J.C. Sivells, Design of two-dimensional continuous-curvature supersonic nozzles. J. Aeronaut. Sci., 22,No. 10, pp. 685, 692, 1955.
J. Ruptash, Supersonic wind tunnels-theory, design and performance, UTIA Review No. 5, 1952.
J.C. Sivells , A Computer Program For The Aerodynamic Design OfAxisymmetric And Planar of NozzlesFor Supersonic And Hypersonic Wind Tunnels, Aedc,Dec1978
E.W.E. Rogers and. Miss B. M. Davis. A note on turbulent boundary layer allowances in supersonicnozzle design. A.R.C.C.P. 333, 1957.
References
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THANKS!!!
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Boundary layer correction
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Boundary layer correction
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Boundary layer correction
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Boundary layer correction
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Boundary layer correction